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A generalized Drude–Lorentz model for refractive index behavior of tellurite glasses

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Abstract

An extension of Drude–Lorentz model based on the fractional approach was used to investigate quantitative measurement of refractive index as a function of wavelength of Tellurite glasses. Tellurite glass samples were synthesized by conventional melt-quenching method with the composition of 65TeO2–15Li2O–20ZnO undoped and doped with different concentrations of Er2O3. Refractive index measurements were performed using the Brewster angle technique with polarized lasers at 442, 532, 594 and 633 nm as light source. From the Sellmeier’s coefficient it was possible to obtain the behavior of refractive index from 0.35 to 1.8 μm. The analytical solution obtained from the generalized Drude–Lorentz model was used to investigate the experimental data of refractive index behavior obtained by the two-pole Sellmeier’s equation showing that the mean polarizability increases with Er2O3 concentration and this behavior can be related to a collective fractal character of the material.

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References

  1. A. Mori, Y. Ohishi, S. Sudo, Erbium-doped tellurite glass fibre laser and amplifier. Electron. Lett. 33(10), 863 (1997)

    Article  CAS  Google Scholar 

  2. J. Wang, E. Vogel, E. Snitzer, Tellurite glass: a new candidate for fiber devices. Opt. Mater. 3(3), 187 (1994)

    Article  CAS  Google Scholar 

  3. S. Shen, A. Jha, X. Liu, M. Naftaly, K. Bindra, H.J. Bookey, A.K. Kar, Tellurite glasses for broadband amplifiers and integrated optics. J. Am. Ceram. Soc. 85(6), 1391 (2002)

    Article  CAS  Google Scholar 

  4. D. Zhou, R. Wang, Z. Yang, Z. Song, Z. Yin, J. Qiu, Spectroscopic properties of Tm3+ doped TeO2–R2O–La2O3 glasses for 1.47 μm optical amplifiers. J. Non-Cryst. Solids 357(11–13), 2409 (2011)

    Article  CAS  Google Scholar 

  5. L.R. Kassab, M.J. Bell, Lanthanide-Based Multifunctional Materials (Elsevier, Amsterdam, 2018), pp. 263–289

    Book  Google Scholar 

  6. N. Jaba, A. Kanoun, H. Mejri, A. Selmi, S. Alaya, H. Maaref, Infrared to visible up-conversion study for erbium-doped zinc tellurite glasses. J. Phys. 12(20), 4523 (2000)

    CAS  Google Scholar 

  7. J. Stanworth, Tellurite glasses. Nature 169(4301), 581 (1952)

    Article  CAS  Google Scholar 

  8. R.A. El-Mallawany, Tellurite Glasses Handbook: Physical Properties and Data (CRC Press, Boca Raton, 2016)

    Book  Google Scholar 

  9. G.N. Conti, V.K. Tikhomirov, M. Bettinelli, S. Berneschi, M. Brenci, B. Chen, S. Pelli, A. Speghini, A.B. Seddon, G.C. Righini, Characterization of ion-exchanged waveguides in tungsten tellurite and zinc tellurite Er3+-doped glasses. Opt. Eng. 42(10), 2805 (2003)

    Article  Google Scholar 

  10. A. Gonçalves, V.S. Zanuto, G.A.S. Flizikowski, A.N. Medina, F.L. Hegeto, A. Somer, J.L. Gomes Jr., J.V. Gunha, G.K. Cruz, C. Jacinto, N.G.C. Astrath, A. Novatski, Luminescence and upconversion processes in Er3+-doped tellurite glasses. J. Lumin. 201, 110 (2018)

    Article  Google Scholar 

  11. A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23(3), 142 (1973)

    Article  CAS  Google Scholar 

  12. R. Betts, T. Tjugiarto, Y. Xue, P. Chu, Nonlinear refractive index in erbium doped optical fiber: theory and experiment. IEEE J. Quantum Electron. 27(4), 908 (1991)

    Article  CAS  Google Scholar 

  13. A. Hasegawa, F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23(4), 171 (1973)

    Article  Google Scholar 

  14. S. Rida, H. El-Sherbiny, A. Arafa, On the solution of the fractional nonlinear schrödinger equation. Phys. Lett. A 372(5), 553 (2008)

    Article  CAS  Google Scholar 

  15. A. Bhrawy, M. Abdelkawy, A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations. J. Comput. Phys. 294, 462 (2015)

    Article  Google Scholar 

  16. L.R. Evangelista, E.K. Lenzi, Fractional Diffusion Equations and Anomalous Diffusion (Cambridge University Press, Cambridge, 2018)

    Book  Google Scholar 

  17. R.E. Gutierrez, J.M. Rosario, J. Tenreiro Machado, Fractional order calculus: basic concepts and engineering applications. Math. Probl. Eng. (2010). https://doi.org/10.1155/2010/375858

    Article  Google Scholar 

  18. S. Das, A new look at formulation of charge storage in capacitors and application to classical capacitor and fractional capacitor theory. Asian J. Res. Rev. Phys. 1(3), 1 (2018)

    Google Scholar 

  19. G. Baumann, Fractals in Biology and Medicine (Springer, Berlin, 2005)

    Google Scholar 

  20. B.I. Henry, S.L. Wearne, Fractional reaction–diffusion. Physica A 276(3–4), 448 (2000)

    Article  Google Scholar 

  21. R. Metzler, J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339(1), 1 (2000)

    Article  CAS  Google Scholar 

  22. J. Hristov, Derivatives with non-singular kernels from the Caputo–Fabrizio definition and beyond: appraising analysis with emphasis on diffusion models. Front. Fract. Calc. 1, 270 (2017)

    Google Scholar 

  23. S. Burov, E. Barkai, Fractional langevin equation: overdamped, underdamped, and critical behaviors. Phys. Rev. E 78, 031112 (2008)

    Article  CAS  Google Scholar 

  24. S. Burov, E. Barkai, Critical exponent of the fractional Langevin equation. Phys. Rev. Lett. 100, 070601 (2008)

    Article  CAS  Google Scholar 

  25. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 (Elsevier, Amsterdam, 1998)

    Google Scholar 

  26. R. Hilfer, Experimental evidence for fractional time evolution in glass forming materials. Chem. Phys. 284(1–2), 399 (2002)

    Article  CAS  Google Scholar 

  27. M. Di Paola, A. Pirrotta, A. Valenza, Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results. Mech. Mater. 43(12), 799 (2011)

    Article  Google Scholar 

  28. J.R. Reitz, F.J. Milford, R.W. Christy, Foundations of Electromagnetic Theory (Addison-Wesley Publishing Company, Boston, 2008)

    Google Scholar 

  29. M.N.R. Jauhariyah, W. Setyarsih, M. Yantidewi, A. Marzuki, Cari, in, International Seminar on Sensors, Instrumentation, Measurement and Metrology (ISSIMM) 2016, 71–74 (2016)

  30. A. Novatski, A. Somer, A. Gonçalves, R.L.S. Piazzetta, J.V. Gunha, A.V.C. Andrade, E.K. Lenzi, A.N. Medina, N.G.C. Astrath, R. El-Mallawany, Thermal and optical properties of lithium–zinc–tellurite glasses. Mater. Chem. Phys. 231, 150 (2019)

    Article  CAS  Google Scholar 

  31. T.J. Wang, Z.H. Kang, H.Z. Zhang, Z.S. Feng, F.G. Wu, H.Y. Zang, Y. Jiang, J.Y. Gao, Y. Andreev, G. Lanskii et al., Sellmeier equations for green, yellow, and orange colored Hg Ga 2 S 4 crystals. Appl. Phys. Lett. 90(18), 181913 (2007)

    Article  Google Scholar 

  32. G. Ghosh, Sellmeier coefficients and chromatic dispersions for some tellurite glasses. J. Am. Ceram. Soc. 78(10), 2828 (1995)

    Article  CAS  Google Scholar 

  33. G. Ghosh, Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses. Appl. Opt. 36(7), 1540 (1997)

    Article  CAS  Google Scholar 

  34. H. Desirena, A. Schlzgen, S. Sabet, G. Ramos-Ortiz, E. de la Rosa, N. Peyghambarian, Effect of alkali metal oxides R2O (R = Li, Na, K, Rb and Cs) and network intermediate MO (M = Zn, Mg, Ba and Pb) in tellurite glasses. Opt. Mater. 31(6), 784 (2009)

    Article  CAS  Google Scholar 

  35. R.N. Brown, Material dispersion in heavy metal oxide glasses containing Bi2O3. J. Non-Cryst. Solids 92(1), 89 (1987)

    Article  CAS  Google Scholar 

  36. J. McCloy, B. Riley, B. Johnson, M. Schweiger, H.A. Qiao, N. Carlie, The predictive power of electronic polarizability for tailoring the refractivity of high-index glasses: optical basicity versus the single oscillator model. J. Am. Ceram. Soc. 93(6), 1650 (2010)

    CAS  Google Scholar 

  37. R.D. Shannon, R.C. Shannon, O. Medenbach, R.X. Fischer, Refractive index and dispersion of fluorides and oxides. J. Phys. Chem. Ref. Data 31(4), 931 (2002)

    Article  CAS  Google Scholar 

  38. H. Takebe, S. Pujino, K. Morinaga, Refractive-index dispersion of tellurite glasses in the region from 0.40 to 1.71 μm. J. Am. Ceram. Soc. 77(9), 2455 (1994)

    Article  CAS  Google Scholar 

  39. S. Umar, M. Halimah, K. Chan, A. Latif, Polarizability, optical basicity and electric susceptibility of Er3+ doped silicate borotellurite glasses. J. Non-Cryst. Solids 471, 101 (2017)

    Article  CAS  Google Scholar 

  40. V. Dimitrov, S. Sakka, Electronic oxide polarizability and optical basicity of simple oxides. I. J. Appl. Phys. 79(3), 1736 (1996)

    Article  CAS  Google Scholar 

  41. V. Dimitrov, T. Komatsu, Classification of oxide glasses: a polarizability approach. J. Solid State Chem. 178(3), 831 (2005)

    Article  CAS  Google Scholar 

  42. S. Butera, M. Di Paola, A physically based connection between fractional calculus and fractal geometry. Ann. Phys. 350, 146 (2014)

    Article  CAS  Google Scholar 

  43. V.M. Shalaev, R. Botet, R. Jullien, Resonant light scattering by fractal clusters. Phys. Rev. B 44(22), 12216 (1991)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors thank to FINEP, CAPES, CNPQ and Fundação Araucária for the partial financial support.

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Authors and Affiliations

  1. Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, 87030-900, Brazil

    Anderson Gonçalves, Maurício A. Ribeiro, Jaqueline V. Gunha, Aloisi Somer & Andressa Novatski

  2. Departamento de Física, Universidade Estadual de Maringá, Maringá, PR, 87020-900, Brazil

    Anderson Gonçalves, Vitor S. Zanuto, Nelson G. C. Astrath & Ervin K. Lenzi

  3. Departamento de Eletrônica, Universidade Federal Tecnológica do Paraná, Ponta Grossa, PR, 84016-210, Brazil

    Maurício A. Ribeiro

  4. Departamento de Física, Universidade Federal Tecnológica do Paraná, Ponta Grossa, PR, 84016-210, Brazil

    Daniele T. Dias

  5. Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, 91501-970, Brazil

    Maike A. F. dos Santos

  6. Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, 57072-900, Brazil

    Carlos Jacinto

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  1. Anderson Gonçalves
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Correspondence to Andressa Novatski.

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Gonçalves, A., Ribeiro, M.A., Gunha, J.V. et al. A generalized Drude–Lorentz model for refractive index behavior of tellurite glasses. J Mater Sci: Mater Electron 30, 16949–16955 (2019). https://doi.org/10.1007/s10854-019-01696-0

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